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Equation 2 · Part 5 · What a Particle Detector Actually Measures

Symbol sigma_p

s=qBℓ28p,σpp  ∝  pBℓ2.s = \frac{qB\ell^{2}}{8p}, \qquad \frac{\sigma_p}{p} \;\propto\; \frac{p}{B\ell^{2}} .
σp\sigma_p

What this part means

sigmapa_p occurs above the fraction bar. The numerator is divided by the entire denominator below it.

Its job in the formula

sigmapa_p occurs above the fraction bar. The numerator is divided by the entire denominator below it.

The passage around this formula

Momentum is not measured. Geometry is measured, and momentum is computed from it under an assumed field map. A charged particle in a solenoidal field follows a helix, and the deviation of its path from a straight line over a chord — the sagitta — carries the momentum information: s=qBℓ28p,σpp  ∝  pBℓ2s = \frac{qB\ell^{2}}{8p}, \qquad \frac{\sigma_p}{p} \;\propto\; \frac{p}{B\ell^{2}} . Here s is the sagitta, B the field, ℓ\ell the path length in the field and p the momentum [ 2 ] . Two consequences follow directly and are worth stating plainly, because they explain most of the architecture of a collider detector.

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A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the surrounding passage

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